A sweet but slight new comedy in the old theatrical style

American Dreams Play by Velina Houston. Directed by Samuel P. Barton. The tribulations of the young Japanese wife of a black American GI returning home from the Korean war multiply apace in Velina Houston's ''American Dreams,'' at Theatre Four. Poor Setsuko Banks (Nancy Hamada) encounters not only the hostility of her ignorant sister-in-law (Sandra Reaves-Phillips) but also the rudeness and unwelcome attentions of brother-in-law Manfred (Count Stovall), a boozing wastrel.

Culture shock is the least of Setsuko's troubles as she discovers some of the darker aspects of the American dream in her in-laws' Lower East Side Manhattan apartment.

Yet the exquisitely polite Setsuko encounters kindness as well as animosity. Sister-in-law Blue River Banks (Kim Yancey) does everything possible to make the timid newcomer feel welcome. Setsuko takes some comfort in the gift of a canary and in brief conversations with a homeless black youth who lurks in the street below the Banks's apartment.

An AmerAsian of Japanese, black, and American Indian ancestry, Miss Houston brings her own special insights to what one character calls a ''crayon box'' of racial mixtures. At the same time, she raises a profusion of issues without ever probing any of them very deeply. Her series of fragmentary episodes ending in blackouts tends to resemble soap-opera plotting.

To the extent possible, the genre comedy drama is believably played under Samuel P. Barton's direction. Miss Hamada is particularly touching as the correct but bewildered Setsuko. Mr. Green portrays Creed as an intelligent, devoted, and determined soldier husband. Completing the play's racial palette are Ching Valdes, Walter Allen Bennett Jr., and Ron Auguste. Daniel Proett designed the efficient unit setting, with costumes (including a gorgeous kimono) by Judy Dearing and lighting by Shirley Prendergast. The accompanying effects include a delicate musical theme for Setsuko.